t-test: Statistical Significance of the Coefficients of Regression

Since the coefficients in the regression represent key parameters such as elasticities and cross-elasticities of demand, it is important that we test their statistical significance.

The t-test is used for this purpose. For each coefficient, it tests that the coefficient differs significantly from zero value.

Consider the regression model: $$ y = b_0+b_1 x_1+b_2 x_2+b_3 x_3 \,…$$

For the coefficient b₁, in the above equation:

Null hypothesis H0: b₁ = 0

Alternative hypothesis HA: b₁ <> 0

Relevant test statistic is t = b₁ /σb₁, where σb₁ is the standard error of b₁.

Relevant distribution is the t-distribution, with degrees of freedom = n − (k + 1). Where k is the number of explanatory variables, and n is sample size.

Similar tests are run for b₂, b₃ … to determine the individual significance of X₂ and X₃ in the model.